Factor completely. $-4x^2-28x-48=$
Answer: First, let's factor out the greatest common factor. If the leading coefficient is negative, we'll also factor out $-1$. The result will be something like this, where the blanks are coefficients: $_{\llcorner\!\lrcorner}\!(_{\llcorner\!\lrcorner}\! x^2+\, _{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!)$ Then, we can try to factor the sum like this: $_{\llcorner\!\lrcorner}\!(_{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!) (_{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!)$ Factor out a the greatest common factor The greatest common factor is $4$. Since the leading coefficient is negative, we'll factor out $-4$. $\begin{aligned} &\phantom{=}-4x^2-28x-48 \\\\ &=-4(x^2+7x+12) \end{aligned}$ [How did we find the greatest common factor?] Factor $x^2+7x+12$ $\begin{aligned} &\phantom{=}-4x^2-28x-48 \\\\ &=-4(x^2+7x+12) \\\\ &=-4(x+3)(x+4) \end{aligned}$ [I want to see this step in more detail.] Answer $\begin{aligned} &\phantom{=}-4x^2-28x-48 \\\\ &=-4(x+3)(x+4) \end{aligned}$ [I factored out a positive 4 instead of a negative 4. Is that wrong?]